If you haven't finished the anime series at least, a couple stages and character abilities may be slightly spoilerish. But here is a good video of the game in action (actual music and scenes not included): http://www.youtube.com/watch?v=DV2OAgm-IOw

If you haven't played the game yet, but want to give it a try, I recommend trying out the tutorial just to get an idea of the basic commands. I'd also suggest focusing at first on just how to move around with the 3d Maneuver Gear and dropping onto titans from a roof above, before going for anything fancier. And select the "TPS" camera selection, it should be the easiest to use. (And never use the space bar, fire hooks individually to aim!)